An Introduction to Graphical Methods
Exploring Baseball Data with R
2026-02-26
What Does a Histogram Show?
A histogram shows how the values of one variable are spread out
- Divide the range into equal-width bins (buckets)
- Count how many observations fall in each bin
- Draw a bar — taller bars = more players in that range
Good for answering:
- What is a typical value?
- Are most values bunched together or spread out?
- Are there any extreme outliers?
Home Runs: Most Players Hit Few
Reading the Home Run Histogram
Three things to notice:
1. Where is it tallest? Around 0–10 home runs — most regulars are not power hitters.
2. What is the shape? The bars fall off gradually to the right. This is called a right-skewed distribution.
3. How far does the tail reach? A very small number of players reach 50+ HRs. These are the elite power hitters.
Batting Average Looks Different
Two Very Different Shapes
A few extreme outliers pull the distribution to the right. Most players are near zero; a few are exceptional.
Values spread out roughly equally above and below the average. This bell-like shape is called symmetric.
Small Multiples: Comparing Eras
Notice the thicker right tail in the 2000s panel — the steroid era fingerprint.
What Is a Density Plot?
A density plot is a smoothed histogram
- Instead of bars, it draws a smooth curve
- The height of the curve at any point tells you how many players landed nearby
- The total area under the curve always equals 1
Why use it?
Density plots are better than histograms for comparing two groups — overlapping curves are much easier to read than overlapping bars.
Comparing Two Eras: Home Runs
Reading the Era Comparison
Steroid era (red):
Thicker far-right tail. A handful of players posted historically unprecedented 50–70 HR seasons.
Modern era (blue):
Higher in the 15–30 HR range — more players adopting power-oriented “launch-angle” swings, but fewer extreme outliers.
Batting Average Has Declined
The curves have the same shape but the modern era (dark blue) sits noticeably to the left — the statistical signature of today’s strikeout-heavy, power-first game.
What Does a Scatterplot Show?
A scatterplot shows the relationship between two variables
- One dot per observation (one player-season)
- X position = first variable
- Y position = second variable
- Patterns in the dot cloud reveal relationships
Good for answering:
- Do two variables move together?
- Is the relationship strong or weak?
- Are there any unusual outliers?
Do Power Hitters Strike Out More?
What the Dot Cloud Tells Us
Direction: The cloud trends upward left to right — more strikeouts tends to mean more home runs. Players who swing for the fences also miss more often.
Strength: The relationship is moderate — there is a clear trend but a lot of scatter. Strikeouts do not perfectly predict home runs.
Outliers: The grey box shows elite power hitters: high strikeout totals but also exceptional home run numbers.
Adding a Trend Line
Reading the Trend Line
Rising section: Through most of the data, the trend goes up — power and strikeouts rise together.
Flattening section: At very high strikeout totals (200+), the trend levels off. Too much swinging and missing becomes counterproductive even for power hitters.
Shaded band: This is the 95% confidence interval — the range of plausible trend lines. Wider band = less certainty.
Colouring by a Third Variable
What the Colours Reveal
Dark blue (walks often) clusters near the top of the plot — combining home run power with plate discipline.
These are the most dangerous hitters. Pitchers cannot simply avoid the strike zone (the batter will take a walk), so they must attack — and get punished when they make a mistake.
Red (rarely walks) spreads broadly — many free swingers strike out often without generating home runs in return.
A Negative Relationship
A strikeout is, by definition, an at-bat with no hit — so more strikeouts directly pull batting average down. But there is still a lot of scatter around the trend.
Positive vs Negative Relationships
A trend line that slopes up = positive relationship. A trend line that slopes down = negative relationship. The steeper the slope, the stronger the relationship.